jmc

Let $a$ denote the price of a sack of apples, $b$ the price of a bunch of bananas, $c$ the price of a cantaloupe, and $d$ the price of a carton of dates. We can express the information given in the problem by the following system of linear equations: $$\begin{array}{rl}a+b+c+d& =20\\ 2a& =d\\ a-b& =c\end{array}$$

Substituting into the first equation for $c$ and $d$ gives $a+b+a-b+2a=20$, which simplifies to $4a=20$, so $a=5$. From here, we use $a$ to find $d=2\cdot 5=10$. We put these values into the first equation to get $5+b+c+10=20$, so b + c = \boxed{ \ 5}$.